Roger can run one mile in 21 minutes. Jeff can run one mile in 18 minutes. If Jeff gives Roger a 1 minute head start, how long will it take before Jeff catches up to Roger? How far will each have run?

Step-by-step explanation:

Step 1

Data of Roger,

Roger runs 1 mile in 21 minutes.

So, Rate by which Roger is running = 1/21 mile/ minute.

Let, Roger runs for x minutes.

So, total distance ran by Roger = rate * time = x/21 mile.

Step 2

Data of Jeff,

Jeff runs 1 mile in 18 minutes.

So, Rate by which Jeff is running = 1/18 mile/ minute.

As Jeff gives Roger a 1 minute head start, so Jeff will run for (x-1) minutes.

So, total distance ran by Jeff = rate * time = (x-1)/18 mile.

Step 3

Equation:

distance = distance

x/21 = (x-1)/18

18x = 21x-21

3x = 21

x = 7 minutes (Roger time)

Roger will run rt = (1/21)7= 1/3 mile

x-1 = 6 minutes (Jeff time)

Jeff will run rt = (1/18)6 = 1/3 mile

i believe it's a.

i'm not sure on this one, most likely correct.